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A compound microscope is an instrument that consists of two lenses L1 and L2. The lens L1 called objective forms a real, inverted and magnified image of the given object. This serves as the object for the second lens L2; the eyepiece. The eyepiece functions as a simple microscope or magnifier. It produces the final image, which is inverted with respect to the original object, enlarged and virtual.

If the power of the eyepiece (L2) is 5 diopters and it forms an image at a distance of 80 cm from its optical centre, at what distance should the object be?

  1. 12 cm
  2. 16 cm
  3. 18 cm
  4. 20 cm

Refraction Lens

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Answer

16 cm

Reason — Given,

Power = +5D [convex lens has positive sign]

v = -80 cm.

u = ?

From formula,

P = 100f(cm)\dfrac{100}{\text{f(cm)}}

Substituting we get,

5 = 100f\dfrac{100}{f}

f = 1005\dfrac{100}{5} = 20 cm

Using formula,

1f\dfrac{1}{\text{f}} = 1v\dfrac{1}{\text{v}} - 1u\dfrac{1}{\text{u}}

We get,

120\dfrac{1}{\text{20}} = 1-80\dfrac{1}{\text{-80}} - 1u\dfrac{1}{\text{u}}

1u\dfrac{1}{\text{u}} = -180\dfrac{1}{\text{80}} - 120\dfrac{1}{\text{20}}

1u\dfrac{1}{\text{u}} = −1−480\dfrac{-1-4}{\text{80}} = −580\dfrac{-5}{\text{80}}

1u\dfrac{1}{\text{u}} = −116-\dfrac{1}{\text{16}}

u = -16

Hence, distance of the object from the lens = 16 cm.

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